A rectangular park measuring 32 yards by 24 yards is surrounded by a trail of uniform width. If the area of the park and the trail combine is 1748 square yards, what is the width of the park

The width = 38 yard

Step-by-step explanation:

Given

Dimension of Park = 32 by 24 yard

Area = 1748 yd²

Required

Find the width of the park

Given that the park is surrounded by a trail;

Let the distance between the park and the trail be represented with y;

Such that, the dimension of the park becomes (32 + y + y) by (24 + y + y) because it is surrounded on all sides

Area of rectangle is calculated as thus;

Area = Length * Width

Substitute 1748 for area; 32 + 2y and 24 + 2y for length and width

The formula becomes

Open Bracket

Subtract 1748 from both sides

Rearrange

Divide through by 4

Expand

Factorize

Split the above into two

But y can't be less than 0;

Recall that the dimension of the park is 32 + 2y by 24 + 2y

So, the dimension becomes 32 + 2*7 by 24 + 2*7

Dimension = 32 + 14 yard by 24 + 14 yard

Dimension = 46 yard by 38 yard

Hence, the width = 38 yard

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

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